I mainly dealt with them as Militant in the Labour Party throughout the 1980s and into the 1990s. They had many good well-meaning activists but to be frank as a group they were awful. They had the worst line of all the left groups on women's liberation and gay rights, arguing that these were "petit bourgeois deviations" from the economic struggle. They opposed Black sections in the Labour Party and were against black self-organisation in general.
They argued a very narrow economistic line that for every political problem the solution was "nationalisation of the commanding heights of the economy, through an enabling bill introduced into parliament by a Socialist Labour government". They characterised every other left group as "a petit bourgeois sect on the fringes of the Labour movement" (these are genuine quotes heard regularly by the way) and aggressively opposed anything that did not come through the official channels of the Labour movement or their own various front movements. Sometimes called "Robo-trot" because of their irritating habit of copying their central leader Ted Grant, who spoke by moving his arm up and down in rhythm with his monotonous delivery, his LPYS rally speeches and the sycophantic reception he got was a signt to behold. They had an awful position on Ireland, arguing for artificial unity between protestant and catholic workers on economic issues and avoiding the national question altogether. They created an international movement in their own image as a satellite from London, having left the Fourth International in 1964 (they claim to have been excluded but really they opted out in my view).
Clearly they became very large - having 3 MPs, leading two national trade unions and having members on the TUC General Council, having about 100 councillors, and a representative on the NEC of the Labour Party. Obviously it is best known that they led Liverpool City Council though the reality is more complex and the legacy of the struggle not so good. Heavily witch-hunted by the right wing in the Labour Party, though they were not really prevented from operating.
After the early 1990s they changed dramatically. They split with their leader for 40 years, Ted Grant, who formed the group Socialist Appeal. Left the Labour Party, became very good on women and gay rights, took up violence against women politically, began to work with other left groups, particularly through the "Network of Socialist Alliances" in the late 1990s.
While all this was healthy, I still have three main criticisms:
1) they still prefer to work through front groups, rather than genuine unity with other left wingers, and are rarely prepared to work in a situation where they are the minority and not in control; their exit from the Socialist Alliance was totally unnecessary and badly handled
2) having had a dodgy position in which they had illusions in the Labour Party and parliament, talking of a "Socialist Labour Government", they now have an ultra left position on the Labour Party, writing off all the left and even standing against John McDonnell in General Elections
3) while their international co-thinkers are now a more diverse bunch and there are some aspects of a debate, there is still a tendency for them to have uniform views and while proclaiming to be trotskyists they still ignore the largest group of trotskyists, without anything that amounts to a principled as opposed to tactical reason for their seperation from the Fourth International.